The C∗-algebra generated by the left-regular representation of ℕn twisted by a 2-cocycle is a Toeplitz extension of an n-dimensional non-commutative torus, on which each vector r ∈ [0,∞)n determines a one-parameter subgroup of the gauge action. I will report on joint work with Z. Afsar, J. Ramagge and M. Laca, in which we show that the equilibrium states of the resulting C∗-dynamical system are parametrized by tracial states of the non-commutative torus corresponding to the restriction of the cocycle to the vanishing coordinates of r. These in turn correspond to probability measures on a classical torus whose dimension depends on a certain degeneracy index of the restricted cocycle. Our results generalize the phase transition on the Toeplitz non-commutative tori used as building blocks in work of Brownlowe, Hawkins and Sims, and of Afsar, an Huef, Raeburn and Sims.
This video was produced by Newcastle University, Australia, as part of the Symmetries in Newcastle seminar series.
